Introduction
Global importance of dripping
One to two paragraphs total
- Differentiation of continental crust
- Potential for orogenesis, plateau formation, and uplift
- They explain diverse observations pretty succinctly (thin Ls, volcanism, basin formation and inversion)
- Scaled down version of Archean tectonics and formation of cratons (e.g. Pilbara)
Have been hypothesized in several locations, but they are difficult to detect and controversial
One paragraph?
- N America
- S America
- Tibet-Himalaya
- Others
And so far, the drips have only been considered in isolation
One paragraph
- why is this an important gap, why is it holding us back
- Maybe have a strong quote here
Goals
One paragraph
- Synthesize the literature on lithospheric dripping to determine whether these drips follow patterns that would be expected from physics and numerical models
- If so, can the drips be classified or grouped?
- Evaluate the strength of evidence for individual drips, especially compared to each other
- Assess the importance of dripping in regards to the initial paragraph \ref{519912}
- Identify future research locations, methods, or observations that will advance our understanding
Mechanisms (physics) of foundering
Rayleigh-Taylor instability (RTI)
- Governing equations - Navier-Stokes
- Growth rate \(\Psi(x, z, t) = Ae^{-\alpha|z|}\exp\left[i\alpha(x-ct)\right]\)
- Assumptions - fluid behaviour of 2 layers with a perturbed interface, etc. Applies equally to layers of gases, liquids, or viscous solids.
- Basic scalings - density contrast and wavelength per unit thickness
- Review papers that have applied these equations to the lithosphere (e.g., \citealp*{Conrad1997}).
- Result - drips are expected to be 100 km in wavelength, but could be larger if background strain rate (shortening) is high
- Limitations (which leads into models) - boundary conditions, complicated rheologies
Several mechanisms for lithospheric foundering have been proposed in the literature. The most common is the Rayleigh-Taylor instability (RTI), also known as gravitational instability, convective instability, or dripping \citep*{Houseman_1981}. In general, the RTI occurs when a fluid of greater density overlies a fluid of lesser density in a force field such as gravity, and refers to the unstable position of the interface between these fluids \citep{Chandrasekhar1961a}. In earth science, the RTI has been most widely used to model mantle plumes, which occur at the core-mantle boundary and ascend through the mantle. In the case of lithospheric foundering, the RTI may occur in the lower crust or mantle lithosphere and descend through the asthenosphere. The density inversion could occur by thickening of the crust and mantle lithosphere, which would push cold, dense lithosphere into warm, less dense asthenosphere \citep*{Houseman_1981}. Eclogitization of the lower crust could accompany thickening, which would increase its density beyond that of peridotite \citep*{Kay_1993}. Dense material could also form in the roots of arc batholiths as garnet pyroxenite restites or cumulates, called arclogites \citep*{Anderson_2005}.
Dense material overlying lighter material is an unstable configuration, one that can be triggered to reorganize through RTI. One trigger is a perturbation of the interface between the two layers. In this case, linear stability analysis is a useful way to understand what happens. Linear stability analysis begins with a small sinusoidal perturbation of the fluid interface for a set of initial and boundary conditions and asks which wavelength of perturbation will grow fastest. The fastest growing wavelength in the initial stages of instability will come to dominate other wavelengths and will lead to the development of drips with a characteristic spacing. Linear instability analysis also gives a function for the growth rate of this wavelength, at least during the early stages of instability.